Half Life or any game made from it. (TFC, CS)
Old Elder Scroll games.
Metal Gear.
Duke Nukem 3D / Shadow Warrior.
Diablo.
Goldeneye.
Smash Bros.
Golden Sun.
F-Zero X.
A Zelda game with gameplay similar to Ocarina of Time.

Lastly: Like so many of us, I too used to play Runescape back in the day. I think it would be a wonderful game to port, if only it could be done. Though it seems like a waste to play on a modern computer, in my opinion, it would make for great Wi-Fi.

Some games I'd like have been mentioned already. What I REALLY want is a remake of Mario RPG Legend Of The Seven Stars. Not a VC emulated version, but an overhaul.

In my opinion, the best way to take upon this undertaking would be to use the graphics engine seen in the DS remakes of Dragon Quest 4 and 5. Using a 3D rotatable world and 2D sprites. Just look at how nice Dragon Quest 4 worked using this:

More frames of animation in the sprites would be nice too. I guess battle could either stay mostly the same with some touch ups, or maybe in a 2D-3D hybrid.

Maybe I'll make a mockup and overlay Mario RPG sprites the that DQ4 image to see what it looks like!

Still, the art needs changing. I just think it's a damn fine graphics engine to use. Being able to rotate the camera would likely be a godsend for some of the platforming parts. And maybe we could finally see those mysterious people who like to hang out behind buildings in the game.